Sensitivity to coefficients

Secondly, the sensitivity of the system performance to system coefficients is exam- ined. It reveals interactions of three objective functions. Three system coefficients, which relates to optimization variables, are analysed in a certain range: the bonus coefficient µ, the compensation coefficient α, and the inelasticity coefficient of de- mand ε.

Sensitivity to bonus coefficient µ

The bonus coefficient µ indicates how would utility share the cost saving with the DR aggregator, where µ ∈ (0, 1]. When µ = 0, it means there is no bonus to the DR aggregator, therefore indicates no DSM is implemented in the system. When µ = 1, it means the utility does not focus on the cost saving from DSM, but concerns the improvement of power system. To analyse it, the bonus coefficient µ is increased from 10% to 100% by the step of 10%, and other coefficients remain the same as stated in Section 3.4.

Table 3.4 shows the detailed beneficial of three participants. It is clear that, as µ increases, the utility’s saving decreases, while the DR aggregator’s profit increases. However, the bill reduction for customers does not change apparently with µ, which

3.5. Sensitivity Analysis Results 61 Table 3.4: The system performance with the change of bonus coefficient µ

µ Utility’s Saving(£) Aggregator’s profit(£) Bill Reduction(£)

10% 133257 8057 1098 20% 118471 22873 1096 30% 103025 37628 1100 40% 88845 52075 1098 50% 73992 67271 1101 60% 59227 82087 1097 70% 44418 96893 1098 80% 29631 111785 1100 90% 14813 125848 1096 100% 0 141328 1099

means the bonus coefficient would not influence customers’ behaviour. Therefore the demand profile would not change apparently with µ, neither does the generation schedule. So µ only reflects the interaction between the utility and the DR aggrega- tor, while the power system would not respond to it. If µ increases, it simply implies the utility is willing to share more of the cost saving to the DR aggregator. Even if the utility gives out all the cost saving, it could not boost the market and result in an improvement of the power system.

Sensitivity to compensation coefficient α

The compensation coefficient α indicates how would the DR aggregator encourage customers to involve in the DSM, where α > 0. To analyse it, the compensation coefficient α is increased from 0 to 10, and other coefficients remain the same as stated in Section 3.4. Between the range of 0 to 1, the coefficient is increased by the step of 0.2, while between the range of 1 to 10, the coefficient is increased by the step of 1.

3.5. Sensitivity Analysis Results 62 0 1 2 3 4 5 6 7 8 9 10 Compensation Coefficient α 3.5 4 4.5 5 5.5 6 Utility Saving [£] ×104

(a) Utility’s Saving VS α

0 1 2 3 4 5 6 7 8 9 10 Compensation Coefficient α 0.8 0.9 1 1.1 1.2 1.3 Aggregator Beneficial [£] ×105 (b) Aggregator’s Profit VS α 0 1 2 3 4 5 6 7 8 9 10 Compensation Coefficient α 600 800 1000 1200 1400 1600 1800 Bill Reduction [£] (c) Bill reduction VS α 0 1 2 3 4 5 6 7 8 9 10 Compensation Coefficient α 1.16 1.161 1.162 1.163 1.164 1.165 1.166 PAR (d) PAR VS α

Figure 3.13: The system performance with the change of compensation coefficient α

3.5. Sensitivity Analysis Results 63 Fig. 3.13 shows the detailed beneficial of three participants and the power system PAR. At the same level of demand adjustment, a larger α means a less compensation would be paid to customers. At the same amount of compensation, a larger α means a higher level of demand adjustment from customers is needed. As α increases, cus- tomers’ bill reduction decreases. Between the range of 0.2 to 1, the utility’s saving and the DR aggregator’s profit increases, while the power PAR decreases. The drop- ping of PAR indicates the extent of demand shift from peak time to off-peak time is raising. Between the range of 1 to 10, the utility’s saving and the DR aggrega- tor’s profit decreases, while the power PAR increases. The raising of PAR indicates the extent of demand shift from peak time to off-peak time is dropping. Based on simulation results, paying less to customers would not help the DR aggregator to increase its net profit. To promote the normal operation of the market, a suitable compensation rate should be designed.

Sensitivity to inelasticity coefficient ε

The inelasticity coefficient ε indicates how would customers react to the inconve- nience that caused by the DSM, where ε > 0. The inelasticity coefficient is related to customers’ preference and the installed appliance. To analyse it, the compensation coefficient µ is increased from 1 to 10 by the step of 1, and other coefficients remain the same as stated in Section 3.4.

Fig. 3.14 shows the detailed beneficial of three participants and the power system PAR. At the same level of demand adjustment, a larger ε means customers are more sensitive, that a higher level of inconvenience would be caused. The inelasticity coefficient varies for customers. For the extreme case, some customers are mainly focused on the QoE and would resist to the demand adjustment. As ε increases, the utility’s saving, the DR aggregator’s profit and bill reduction decrease, while PAR increases. When the inconvenience caused by the DSM is significant, customers are reluctant to take part in the market, thus the DSM is hard to implement. In this situation, the adjustable ability of demand is restricted, and the system improvement is limited.

3.5. Sensitivity Analysis Results 64 0 1 2 3 4 5 6 7 8 9 10 Inelasticity Coefficient ǫ 4.2 4.3 4.4 4.5 4.6 4.7 Utility Saving [£] ×104

(a) Utility’s Saving VS ε

0 1 2 3 4 5 6 7 8 9 10 Inelasticity Coefficient ǫ 9.2 9.4 9.6 9.8 10 Aggregator Beneficial [£] ×104 (b) Aggregator’s Profit VS ε 0 1 2 3 4 5 6 7 8 9 10 Inelasticity Coefficient ǫ 1000 1050 1100 1150 Bill Reduction [£] (c) Bill reduction VS ε 0 1 2 3 4 5 6 7 8 9 10 Inelasticity Coefficient ǫ 1.161 1.162 1.163 1.164 PAR (d) PAR VS ε

3.6. Chapter Summary 65

3.6

Chapter Summary

This chapter proposed a hierarchical framework for the electricity market. The framework consisted of the utility, the DR aggregator, and customers. The role of the DR aggregator was defined as an intermediary communicating with both the utility and customers. The modelled system led to a MOP, which can be solved by the AIA. Through the proposed AIA, the APS was obtained. After that, a Pareto optimal solution was selected that maximizes the minimum improvement in all di- mensions. The simulation results showed that all participants can benefit from the proposed design: the utility can reduce the generation cost and the power PAR; the DR aggregator can make a profit by providing DSM service; customers can save money on their bill. Even if there were perturbations to the system, the proposed approach can still work out an optimal solution. As the bonus coefficient µ increased, the DR aggregator’s net income also increased, while the utility’s generation cost saving decreased. As the compensation coefficient α increased, customers’ bill re- duction decreased. When the power PAR decreased, the utility’s saving and the DR aggregator’s profit increased, and vice verse. As the inelasticity coefficient ε in- creased, the utility’s saving, the DR aggregator’s profit and customers’ bill reduction decreased, while the power PAR increased.

Chapter 4

Power Generation Scheduling and

Operational Policy Making

4.1

Introduction

To effectively achieve the carbon emission reduction, a system model is established in this chapter, which consists of policy makers, utilities and consumers. Policy makers aim for minimizing the carbon emission, and making sure a certain penetration of RESs is reached. Utilities try to maximize the net profit of electricity supply, on the premise of system stability. Consumers seek to minimize the electricity bill, and receive an acceptable quality of electricity service. This model leads to a MOP. After obtaining the APF, a MMD approach is proposed to select the final solution. This proposed method is then compared with existing approaches, i.e., the WS approach and D & C approach. The case studies of short-term period and long-term period are presented. These case studies prove that these three approaches can work out a same solution. But the proposed MMD approach does not require priority information before selection, and does not need to differentiate objective functions, which make it can be widely used. The selected solution in short-term period case study suggests reductions in the use of coal and gas, while raises in nuclear and wind. For long-term period case study, the use of wind, nuclear and bioenergy are suggested to take the dominant status, while the use of coal, oil and gas are negligible. Then, system sensitivities to several coefficients are analysed. Overall, the main contributions of

4.2. System Model 67 this chapter can be summarized as below:

• Besides economic and environmental aspects of the electricity generation, the participation of consumers is introduced in the system model.

• A MMD approach is proposed to process the MCDM, compared with D & C approach and WS approach.

• The practical U.K. case studies are conducted to illustrate the proposed model and approach. The generation plans for both short-term period and long-term period are presented.

• The impact of carbon tax and Renewable Obligation on carbon emission, gen- eration cost and electricity bill are examined. These can reveal the proper strategy for deciding RESs and carbon emission related policies.

The chapter is organized as follows. Section 4.2 introduces a system model, which includes policy makers, utilities and customers. Section 4.3 illustrates the proposed MMD approach for MCDM, compared with D & C approach and WS approach. Section 4.4 provides the comparative analysis among three approaches. Section 4.5 presents the simulation results. Section 4.6 tests the system sensitivity. Finally, Section 4.7 concludes this chapter.

4.2

System Model

In this section, the system operational model is introduced. The framework is presented in Fig. 4.1. Policy makers set the carbon allowance and the RESs re- quirement. Utilities provide the electricity to consumers, and carry out the carbon emission reduction. They also encourage consumers to participate in DSM programs. Consumers use the electricity and are involved in the energy market [52].

4.2. System Model 68

Figure 4.1: The system operation model.